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In recent decades, advancements in information technology allowed Artificial Intelligence (AI) systems to predict future outcomes with unprecedented success. This brought the widespread deployment of these methods in many fields, intending to support decision-making. A pressing question is how to make AI systems robust to common challenges in real-life scenarios and trustworthy. In my work, I plan to explore ways to enhance the trustworthiness of AI through the selective classification framework. In this setting, the AI system can refrain from predicting whenever it is not confident enough, allowing it to trade off coverage, i.e. the percentage of instances that receive a prediction, for performance.